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Remarks on the naturality of quantization

T. Foth·A. Uribe
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Abstract

Hamiltonian quantization of an integral compact symplectic manifold M depends on a choice of compatible almost complex structure J. For open sets U in the set of compatible almost complex structures and small enough values of Planck's constant, the Hilbert spaces of the quantization form a bundle over U with a natural connection. In this paper we examine the dependence of the Hilbert spaces on the choice of J, by computing the semi-classical limit of the curvature of this connection. We also show that parallel transport provides a link between the action of the group Symp(M) of symplectomorphisms of M and the Schrodinger equation.

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T. Foth, A. Uribe. 2004-10-01. Remarks on the naturality of quantization. https://doi.org/10.1007/s00220-007-0280-9

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